Optimal designs for indirect regression

In many real life applications, it is impossible to observe the feature of interest directly. For example, non-invasive medical imaging techniques rely on indirect observations to reconstruct an image of the patient's internal organs. In this paper, we investigate optimal designs for such indirect regression problems. We use the optimal designs as benchmarks to investigate the efficiency of designs commonly used in applications. Several examples are discussed for illustration. Our designs provide guidelines to scientists regarding the experimental conditions at which the indirect observations should be taken in order to obtain an accurate estimate for the object of interest. Moreover, we demonstrate that in many cases the commonly used uniform design is close to optimal.